Among the many contentious exchanges in Tuesday's presidential debate was a barbed back-and-forth between Mitt Romney and President Barack Obama about the size and contents of their pensions plans.

"Mr. President, have you looked at your pension? Have you looked at your pension?”

“I don’t look at my pension. It’s not as big as yours so it doesn’t take as long.”

“Let me give you some advice. You also have investments in Chinese companies. You also have investments outside the United States.”

Romney is right, Obama does have a small portion of investments in companies outside the U.S. through a pension fund worth $50,000 to $100,000 that he earned while he was state senator of Illinois.

Obama also has investments in things that are counter to his political positions. A look under the hood of his pension fund reveals investments in controversial for-profit colleges and companies that support anti-abortion causes (see below).

Pension funds, similar to other huge mutual funds, contain a huge mix of diverse investments in domestic and foreign firms. Investors don't actively manage these funds. Rather, they are run by managers, who buy or sell the shares.

With broad funds, like pensions funds or ones that follow the Standard & Poor's 500, you "may have some questionable options and for better and worse that gives diversification," said Brooks Herman, head of research at BrightScope, a financial information company.

The fact that either Romney or Obama have some investments in Chinese companies actually only represents a decent, well-diversified investment strategy.

However, Romney's comparison of his own investments -- primarily a blind trust that is worth up to $250 million -- to Obama's modest pension is somewhat flawed.

For starters, the size of the investments is vastly different. Romney's critics have charged that the Republican's trust is not blind, makes use of offshore investments and contains plenty of stocks in companies that are not Republican-friendly, like pharma companies doing stem-cell research or Chinese oil companies who have been close with Iran. The candidate's timing also smells funny: Romney dropped a number of controversial investments on Aug. 10, 2011, the night before he took part in a Republican primary debate in Iowa.

For Obama, his pension represents a small fraction of his wealth. According to the Obama's most recent tax return, the first couple also has about $325,000 invested in a Vanguard index fund. They also have nearly $5 million in cash investments, according to Kiplinger.

Here are 10 investments inside Barack Obama's pension:

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10 Companies Inside Obama's Pension Fund

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Among the holdings in the Illinois pension are shares of the Las Vegas Sands corporation, owned by mega GOP donor Sheldon Adelson. The casino magnate has given tens of millions to Republican PACs; the company is also facing investigation for various illegal operations at the casino's Macau location.

The Illinois pension has some shares of Domino's Pizza in its investment mix. The company's founder, a devout Catholic, has supported anti-abortion groups in the past and held mass in the company's conference rooms. Obama supports pro-choice legislation.

DeVry Inc., makes up a healthy portion of the Illinois Pension fund, and is one of the biggest for-profit universities. The sector is highly subsidized by the government and has contributed to the more than $1 trillion in student loan debt -- an issue Obama has vowed to improve.

The largest life insurance company in China is just one of several China-based holdings in the Illinois pension plan, according to the annual report. Mitt Romney recently unloaded his China Life Insurance shares along with many other Chinese investments.

Exxon Mobil is just one of several energy companies in which the pension owns shares. The oil giant not only has a very tarnished environmental record -- even funding climate skeptic groups -- it also collects huge tax breaks from the government that Obama has tried to kill.

The pension contains share of Halliburton, which was once helmed by former vice president Dick Cheney. The company has been awarded multiple no-bid contracts for multi-million projects by the government, a practice Obama has railed against in the past.

The pension contains shares of Altria, the investor-friendly name for tobacco company Philip Morris USA. Not only do cigarettes cause cancer and other life-threatening diseases, the tobacco industry conspired to hide damning evidence about their product from the government, a judge ruled in 2006. Obama has reportedly quit smoking.

Giant payday lender Cash America make ups only a tiny portion of stock listed in the pension fund, but payday lenders have drawn ire from consumer advocates for their extremely high interest rates and high fees, and have been banned in many cities and some states for unfair lending practices. Under Obama's watch, the Consumer Financial Protection Bureau has vowed to crack down on payday lenders.

The pension fund includes shares in the food conglomerate, which makes many kinds of prepared snacks foods that are high in fat, sugar and salt, like Reddi Wip. In other words, everything that Michelle Obama has actively campaigned against with her anti-childhood obesity program.

The pension fund includes shares of Apple. The tech company's Chinese manufacturer Foxconn has come under increasing scrutiny for itslabor practices. The company has also sent thousands of jobs to China. “Apple’s an example of why it’s so hard to create middle-class jobs in the U.S. now,” Jared Bernstein, who was an economic adviser to the White House until 2011, told the New York Times.